In this article, you will learn how to find a Matrix that is Symmetric Matrix or not using Java. A symmetric matrix is a square matrix that remains unchanged when transposed (rows become columns, and vice versa).
Symmetric Matrix: A symmetric matrix is a square matrix where the element at the ith row and jth column is equal to the element at the jth row and ith column. In other words, if A is a symmetric matrix, then A[i][j] = A[j][i] for all i and j. Consequently, the matrix A is symmetric if its transpose is equal to itself, i.e., A^T = A.
For example, consider the following symmetric matrix:
1 2 3
2 4 5
3 5 6
Here, the element at row 1, column 2 (2) is the same as the element in row 2, column 1 (2), and so on.
In Java, symmetric matrices are often represented using a 2D array. The 2D array stores the elements of the matrix, and to check whether the matrix is symmetric, we need to compare each element with its corresponding transposed element. Here’s a Java program to check if a given square matrix is an identity matrix:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 | package com.javacodepoint.array.multidimensional;public class SymmetricMatrix { public static boolean isSymmetric(int[][] matrix) { int rows = matrix.length; int cols = matrix[0].length; // Check if the matrix is square if (rows != cols) { return false; } // Compare each element with its transposed element for (int i = 0; i < rows; i++) { for (int j = i + 1; j < cols; j++) { if (matrix[i][j] != matrix[j][i]) { return false; } } } return true; } public static void main(String[] args) { int[][] matrix1 = { { 1, 2, 3 }, { 2, 4, 5 }, { 3, 5, 6 } }; int[][] matrix2 = { { 1, 2, 3 }, { 4, 5, 6 }, { 7, 8, 9 } }; System.out.println("Matrix:"); for (int[] row : matrix1) { for (int value : row) { System.out.print(value + " "); } System.out.println(); } System.out.println("Is Symmetric Matrix: "+isSymmetric(matrix1)); System.out.println("Matrix:"); for (int[] row : matrix2) { for (int value : row) { System.out.print(value + " "); } System.out.println(); } System.out.println("Is Symmetric Matrix: "+isSymmetric(matrix2)); }} |
OUTPUT:
Matrix:
1 2 3
2 4 5
3 5 6
Is Symmetric Matrix: true
Matrix:
1 2 3
4 5 6
7 8 9
Is Symmetric Matrix: false
Explanation:
In this program, the static method isSymmetric, first checks if the matrix is square (number of rows equals the number of columns). Then, it compares each element with its corresponding transposed element, starting from the top-right half of the matrix. If any element is found to be different, the matrix is not symmetric.
Learn also: Identity Matrix Program.